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We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac…
Several intriguing electronic phenomena and electric properties were discovered in three-dimensional Dirac nodal line semimetals (3D-DNLSM), which are, however, easy to be perturbed under strong spin-orbit coupling (SOC). While…
A two-dimensional field theory of a fermion chirally coupled to Toda field plus a scalar self-coupling potential is considered. Using techniques of integrable systems we obtain analytical zero modes, in-gap states and bound states in the…
Three-dimensional topological insulators support gapless Dirac fermion surface states whose rich topological properties result from the interplay of symmetries and dimensionality. Their topological properties have been extensively studied…
We consider an extension of a special class of conformal sigma models (`chiral null models') which describe extreme supersymmetric string solutions. The new models contain both `left' and `right' vector couplings and should correspond to…
Since the discovery of graphene, layered materials have attracted extensive interests owing to their unique electronic and optical characteristics. Among them, Dirac semimetal, one of the most appealing categories, has been a long-sought…
We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion. Using the cubic lattice with plaquette $\pi$-flux as a model, we find, among others phases, a chiral topological insulator and singlet topological…
Uncovering the physical contents of the nontrivial topology of quantum states is a critical problem in condensed matter physics. Here, we study the topological circular dichroism in chiral semimetals using linear response theory and…
A 4-dimensional heterotic string model of free fermionic construction is presented wherein mirror symmetry breaking between observable and hidden sector gauge groups occurs in spite of mirror symmetry between observable and hidden sector…
The chiral phase dependence of fermion partition function in spherically symmetric U(1) gauge field background is analyzed in two dimensional space-time. A well-defined method to calculated the path integral which apply to the continuous…
The search for symmetry-protected 2D Dirac semimetals analogous to graphene is important both for fundamental and practical interest. The 2D Dirac cones are protected by crystalline symmetries and magnetic ordering may destroy their…
Domain wall fermions are defined on a lattice with an extra direction the size of which controls the chiral properties of the theory. When gauge fields are coupled to domain wall fermions the extra direction is treated as an internal flavor…
In a dynamical lattice simulation with the overlap Dirac operator and $N_f=2$ mass degenerate quarks we study all possible $J=0$ and $J=1$ correlators upon exclusion of the low lying "quasi-zero" modes from the valence quark propagators.…
Chiral defect fermions in the background of an external, $2n$ dimensional gauge field are considered. Assuming first a finite extra dimension, we calculate the axial anomaly in a vector-like, gauge invariant model for arbitrary $n$, and the…
We study the behavior of neutral meson properties in the presence of a static uniform external magnetic field in the context of nonlocal chiral quark models. The formalism is worked out introducing Ritus transforms of Dirac fields, which…
Edge states are studied for the two-dimensional Dirac equation in a circular geometry. The properties of the two-component electromagnetic field are discussed in terms of the three-component polarization field, which can form a vortex…
We study the properties of low-lying Dirac modes in quenched compact QED at $\beta$=0.99, 1.01 and 1.03, employing $12^3\times 12$ lattices and the overlap formalism for the fermion action. We pay special attention to the spatial…
We analyze zero mode counting problems for Dirac operators that find their origin in string theory backgrounds. A first class of quantum mechanical models for which we compute the number of ground states arises from a string winding an…
Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by…
Rare-earth magnets with parent cubic symmetry exhibit unique topological properties. However, the origin of these behaviors remains presently unclear. Here, we develop minimal models for Dirac semimetals (DSMs) with accidental band…